A battle for the future of the Labour party was blown into the open on Thursday when Tony Blair warned Ed Miliband to avoid a "menacing" scenario in which the party returns to its "comfort zone" to attack all government cuts.

In a carefully worded put-down to the former prime minister, the Labour leader responded by saying he was drawing up plans for the future and was keen to move away from old thinking.

Miliband said: "Tony Blair has always got important things to say. He is the first to recognise that political parties need to move forwards, not backwards, need to not go back to old solutions and need to adapt to new times. On immigration we made mistakes in office. We can't just defend what we did in the past."

The Labour leader spoke out after Blair used an article in the centenary edition of the New Statesman to highlight concerns among his supporters that Miliband mistakenly believes that Britain is responding to the financial crash by turning to the left. Blair also warned that the party must be rooted in the centre ground and must not become a protest party.

The former prime minister wrote: "The guiding principle should be that we are the seekers after answers, not the repository for people's anger. In the first case, we have to be dispassionate even when the issues arouse great passion. In the second case, we are simple fellow-travellers in sympathy; we are not leaders. And in these times, above all, people want leadership."

Blair directly challenged Miliband's belief that the financial crash and the subsequent recession has created an appetite for a remodelling of capitalism from the left. The former premier wrote: "The paradox of the financial crisis is that, despite being widely held to have been caused by under-regulated markets, it has not brought a decisive shift to the left. But what might happen is that the left believes such a shift has occurred and behaves accordingly."

Blair did not say Miliband believes this. But the former prime minister's supporters fear the Labour leader is in the process of making a mistake of historic proportions in believing that the financial crash and a prolonged recession exacerbated by spending cuts have created an appetite for a shift to the left.

Some Blair supporters fear a repeat of 1987 when a reasonably united Labour party, which ran a slick election campaign, went down to a heavy defeat because it failed to tack to the centre.

Blair writes: "Having a modern vision … helps avoid the danger of tactical victories that lead to strategic defeats. It means, for example, that we don't tack right on immigration and Europe, and tack left on tax and spending.

"It keeps us out of our comfort zone but on a centre ground that is ultimately both more satisfying and more productive for party and country."

He says the Tories face a "less menacing" scenario in which they are vilified for spending cuts. But they will say they are restoring order.

But Labour faces a more difficult challenge: "For Labour, the opposite is true. This scenario is more menacing than it seems. The ease with which it can settle back into its old territory of defending the status quo, allying itself, even anchoring itself, to the interests that will passionately and often justly oppose what the government is doing, is so apparently rewarding, that the exercise of political will lies not in going there, but in resisting the temptation to go there."

Blair's article appears as Miliband attends a progressive governance conference in Copenhagen organised by the Policy Network thinktank founded by Lord Mandelson.

The former business secretary, who is the organisation's president, will chair a session on Monday morning in which Miliband will discuss "governing as progressives" with the Danish prime minister Helle Thorning-Schmidt.

Patrick Diamond, who co-wrote the Labour manifesto for the last election with Miliband and who is one of the main figures in Policy Network, writes on the Guardian's Comment is Free website to say that progressives need to take note of Blair's wider call for reforms of the post-1945 political settlement.

In words that will cause little trouble for Miliband, Diamond writes: "Tony Blair argued in his New Statesman article that: 'The systems we created post-1945 have to change radically'. This message should be heeded. The political future of centre-left parties relies on identifying a plausible model of social democracy in hard times serving not only as a strategy in opposition, but as a credible approach in government."

In his article Blair said Labour will win permission to govern only if it provides answers to a series of policy challenges. He lists seven:

• What is driving the rise in housing benefit spending, and if it is the absence of housing, how do we build more?

• How do we improve the skill-set of those who are unemployed when the shortage of skills is the clearest barrier to employment?

• How do we take the health and education reforms of the last Labour government to a new level, given the huge improvement in results they brought about?

• What is the right balance between universal and means-tested help for pensioners?

• How do we use technology to cut costs and drive change in our education, health, crime and immigration systems?

• How do we focus on the really hard core of socially excluded families, separating them from those who are just temporarily down on their luck?

• What could the developments around DNA do to cut crime?

Grant Shapps, the Tory chairman, said: "Tony Blair is right to warn that Labour aren't a credible party of government under Ed Miliband. Ed Miliband and Ed Balls have opposed every single difficult decision this government has taken to fix the problems that Labour left behind - on welfare, on immigration and on the deficit. The only plan Labour have is more of what got us into this mess in the first place - more spending, more borrowing and more debt."